Mathematical models for antibiotic/antimicrobial resistance based on ordinary and partial differential equations (ODE/PDEs) are presented in this book, starting with a basic ODE model in Chapter 1, and concluding with a detailed PDE model in Chapters 4 and 5 that gives the spatiotemporal distribution of four dependent variable components: (1) susceptible bacteria population density, (2) resistant bacteria population density, (3) plasmid number, and (4) antibiotic concentration.
The computer-based implementation of the example models is presented through routines coded (programmed) in R, a quality, open-source scientific computing system that is readily available from the Internet. Formal mathematics is minimized, e.g., no theorems and proofs. Rather, the presentation is through detailed examples that the reader/researcher/analyst can execute on modest computers. The PDE analysis is based on the method of lines (MOL), an established general algorithm for PDEs, implemented with finite differences.
The routines are available from a download link so that the example models can be executed without having to first study numerical methods and computer coding. The routines can then be applied to variations and extensions of the antibiotic/antimicrobial models, such as changes in the ODE/PDE parameters (constants) and the form of the model equations.
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